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Chuanfeng Sun

Publications and source records attributed to Chuanfeng Sun.

8 recordsLinked to original sources
arXiv2026

Revisiting the logical independence

It has been widely acknowledged that probabilistic independence and logical independence cannot be coherently reconciled. By bridging these two notions, this paper addresses three long-standing problems that have puzzled the field of probability theory: Should probability be defined prior to independence, or independence prior to probability? How ought independence to be formulated for signed measures and families of probability measures? Why do the conclusions of classical limit theorems remain valid even when practical scenarios violate their underlying assumptions? By introducing logical independence and $\sigma$-logical independence, we establish the probability extension theorem. This result not only demonstrates that independence ought to be defined before probability, but also endows logical independence with probabilistic machinery, thereby rendering it computationally tractable in the same manner as probabilistic independence. Then, we investigate how independence should be defined when multiple measures are involved. Finally, we prove that limit theorems can hold true under two intuitive conditions: $\sigma$-logical independence and identical range of random variables.

math.PR↗
arXiv2021

A generalized Neyman-Pearson lemma for sublinear expectations

In this paper, the Neyman-Pearson lemma for general sublinear expectations is studied. We weaken the assumptions for sublinear expectations in [1] and give a completely new method to study this problem. Applying Mazur-Orlicz Theorem and the decomposition theorem of finitely additive set functions, we prove that the optimal test still has the reminiscent form as in the classical Neyman-Pearson lemma. Finally, for the special sublinear expectation which can be represented by a family of probability measures, we give a sufficient condition for the existence of the optimal test and show the form of the optimal test selected in L_{c}^1-space which is introduced by Peng [10] in his nonlinear-expectation framework.

math.PR↗
arXiv2020

Kalman-Bucy filtering and minimum mean square estimator under uncertainty

In this paper, we study a generalized Kalman-Bucy filtering problem under uncertainty. The drift uncertainty for both signal process and observation process is considered and the attitude to uncertainty is characterized by a convex operator (convex risk measure). The optimal filter or the minimum mean square estimator (MMSE) is calculated by solving the minimum mean square estimation problem under a convex operator. In the first part of this paper, this estimation problem is studied under g-expectation which is a special convex operator. For this case, we prove that there exists a worst-case prior. Based on this worst-case prior we obtained the Kalman-Bucy filtering equation under g-expectation. In the second part of this paper, we study the minimum mean square estimation problem under general convex operators. The existence and uniqueness results of the MMSE are deduced.

math.OC↗
arXiv2019

The Neyman-Pearson lemma for convex expectations

We study the Neyman-Pearson problem for convex expectations on L^{\infty}(μ). The existence of the optimal test is given. Without assuming that the level sets of penalty functions are weakly compact, we prove that the optimal tests for convex expectations on L^{\infty}(μ) are just the classical Neyman-Pearson tests between a fixed representative pair of simple hypotheses. Then we show that the Neyman-Pearson problem for convex expectations on L^{1}(μ) can be solved similarly.

math.PR↗
arXiv2019

A robust Kalman-Bucy filtering problem

A generalized Kalman-Bucy model under model uncertainty and a corresponding robust problem are studied in this paper. We find that this robust problem is equivalent to an estimate problem under a sublinear operator. By Girsanov transformation and the minimax theorem, we prove that this problem can be reformulated as a classical Kalman-Bucy filtering problem under a new probability measure. The equation which governs the optimal estimator is obtained. Moreover, the optimal estimator can be decomposed into the classical optimal estimator and a term related to model uncertainty.

math.OC↗
arXiv2019

A filtering problem with uncertainty in observation

This paper is concerned with a generalized Kalman-Bucy filtering model and corresponding robust problem under model uncertainty. We find that this robust problem is equivalent to considering an estimate problem under some sublinear operator. Therefore, we turn to obtaining the minimum mean square estimator under a sublinear operator. By Girsanov theorem and minimax theorem, we obtain the optimal estimator $\hat{x}_{t}$ of the signal process $x_{t}$ for given time $t\in\lbrack0,T]$.

math.PR↗
arXiv2015

Two laws of large numbers for sublinear expectations

In this paper, we consider the sublinear expectation on bounded random variables. With the notion of uncorrelatedness for random variables under the sublinear expectation, a weak law of large numbers is obtained. With the notion of independence for random variable sequences and regular property for sublinear expectations, we get a strong one. These results are helpful for the application of the law of large numbers in engineering and statistics such as to assess the level of product quality and to explain the relationship between the statistical distribution and the sample distribution.

math.PR↗